Can games tell stories? Why or why not?

Can games tell stories?  Why or why not?

What stops a game from telling a story? Why do some people play through the most craptastic turn based battle gameplay and horrible graphics to experience a story, while others cannot skip the briefest cinematic quick enough to get back to shooting nazis and terrorists? I think it is a safe assumption that most any gamer likes story (movies, tv, books), just not necessarily in their game.